Correct way to calculate energy in Bohr Atom Model

[Bassalisk]

I was deriving Bohr model formulas and I stumbled upon a problem.

When I use the postulate that says that you can apply Newtonian Mechanics to orbiting electron, I wrote the Coulomb's force as following:


Fc=(-e)*Z*e/(4pi(epsilon0)*r^2)


Minus from the electron means that the force will be attractive. But when I integrated it to get the energy I got a minus from integration. Now if I put in the charges in, I got that minus like from coulombs force and those 2 cancel out, leaving me with positive energy.


I escaped from this by using potential energy as positive and substituting charges like I did in Coulomb's Force, but this is workaround and its not mathematically correct.

I attached a relevant image.

What is full correct way to do this?

 

[jeppetrost]

Since the F = -dV/dr, that would make dV = -F dr. I think you used a plus.

 

[Bassalisk]

Thats by definition? So, I put full charge values into energy too, not by absolute value?

 

[stevenytc]

E_potential = - int Fc dr

please check the definition of potential energy

 

[Bassalisk]

Again, I do enter charges by normal value, not absolute value, that would get rid of minus from the electric charge of electron (-e)?